All categories

3 years ago

The radius of a sphere X is 3 inches, and radius of sphere Y is 9 inches. How many

Mathematics

1 answer:

kirza4 [7]3 years ago

7 0

The volume of the sphere Y is 27 times the volume of the sphere X

Step-by-step explanation:

Sphere X:

Radius of sphere X = 3 inches

Volume = (4/3) π(27)

Sphere Y:

Radius of sphere Y = 9 inches

Volume = (4/3) π(729)

Volume of sphere Y /volume of sphere X = (4/3) π(729) /(4/3) π(27)

= (729) /(27)

= 27

The volume of the sphere Y is 27 times the volume of the sphere X

You might be interested in

A postage stamp has a area 1160mm^2. About how long is each side ?

Savatey [412]

Each side is about 290mm long

4 0

3 years ago

Determine the most precise name for ABCD (parallelogram, rhombus, rectangle, or square). Explain how you determined your answer.

Sonja [21]

<h3>Answer: Rhombus</h3>

======================================================

Reason:

Let's find the distance from A to B. This is equivalent to finding the length of segment AB. I'll use the distance formula.

$A = (x_1,y_1) = (3,5) \text{ and } B = (x_2, y_2) = (7,6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-7)^2 + (5-6)^2}\\\\d = \sqrt{(-4)^2 + (-1)^2}\\\\d = \sqrt{16 + 1}\\\\d = \sqrt{17}\\\\d \approx 4.1231\\\\$

Segment AB is exactly $\sqrt{17}$ units long, which is approximately 4.1231 units.

If you were to repeat similar steps for the other sides (BC, CD and AD) you should find that all four sides are the same length. Because of this fact, we have a rhombus.

-------------------------

Let's see if this rhombus is a square or not. We'll need to see if the adjacent sides are perpendicular. For that we'll need the slope.

Let's find the slope of AB.

$A = (x_1,y_1) = (3,5) \text{ and } B = (x_2,y_2) = (7,6)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{6 - 5}{7 - 3}\\\\m = \frac{1}{4}\\\\$

Segment AB has a slope of 1/4.

Do the same for BC

$B = (x_1,y_1) = (7,6) \text{ and } C = (x_2,y_2) = (6,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - 6}{6 - 7}\\\\m = \frac{-4}{-1}\\\\m = 4\\\\$

Unfortunately the two slopes of 1/4 and 4 are not negative reciprocals of one another. One slope has to be negative while the other is positive, if we wanted perpendicular lines. Also recall that perpendicular slopes must multiply to -1.

We don't have perpendicular lines, so the interior angles are not 90 degrees each.

Therefore, this figure is not a rectangle and by extension it's not a square either.

The best description for this figure is a <u>rhombus</u>.

4 0

2 years ago

Read 2 more answers

Evaluate the expression.<br> 5 - (4 - 2 - (6-6))<br> 8<br> 2<br> 5<br> 3

Doss [256]

Answer: 3

Step-by-step explanation:

5−(4−2−(6−6))

3 0

4 years ago

Read 2 more answers

A cylinder has volume 45 pie and radius 3. What is its height?

liraira [26]

Answer:

5 units

Step-by-step explanation:

The <u>volume of the cylinder</u> is the area of the circle multiplied by it's height. Therefore, the volume of the cylinder is πr² × h, which when simplified, gives us πr²h. Let's substitute the volume and the radius in the formula to find the height.

⇒ πr²h = Volume of cylinder

⇒ (π)(3²)(h) = 45π

Now, simplify the equation to evaluate the area of the cylinder.

⇒ (π)(3²)(h)/(3²)(π) = 45π/(3²)(π)

⇒ (h) = 45π/(9)(π) = 45/(9) = 5 units

7 0

3 years ago

Which below best describes the shape of a large falling raindrop about 5 millimeters in diameter? a. spherical b. square c. tear

Akimi4 [234]

Answer:

slightly elongated and flattened on the bottom

Step-by-step explanation:

When rain falls, it loses that round shape. Raindrops become like the upper half of a hamburger. Flattened at the bottom and with a top arch

7 0

3 years ago